{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15.4. Computing exact probabilities and manipulating random variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from sympy.stats import *\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = Die('X', 6), Die('Y', 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "podoc": {
     "output_text": "1/6"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACoAAACqBAMAAAApXcCwAAAAMFBMVEX///+6uroiIiJmZmZUVFSI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\n",
      "text/plain": [
       "1/6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P(Eq(X, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "podoc": {
     "output_text": "1/2"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACoAAACoBAMAAABklWG7AAAAMFBMVEX///+6uroiIiJmZmZUVFSI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\nXuVyyPXZhg8BKFx4yWuG6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "1/2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P(X > 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "podoc": {
     "output_text": "5/12"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAACpBAMAAABHSQc1AAAAMFBMVEX///92dnaqqqpUVFQiIiKI\niIju7u66uroyMjJERETMzMzc3NxmZmYQEBCYmJgAAAC+O/0eAAAAAXRSTlMAQObYZgAAAAlwSFlz\nAAAOxAAADsQBlSsOGwAAA29JREFUWMPtmT1oU1EUx2/68ZImNe0m4hCNIIJDcLNTOog41L4iLoJo\nBpGCaDu6JVhokQ4pqOCWOCpInwiKiigWJ8Es6uDXq5+LUGsa2zxrPN4kfTfnvvfuBzjY4f2n2/Dr\nzXvnnPvxPyGEU/KtxcbXC0SmfnAm2yPjKMxJ0W4AuLI3Z9z9ZAJYStTVH6KNLmqja0QXdSxdtLaD\nKFG7PaeSpGhi59CBS1sJ0UCJrkJ0c6DXhi4+tXRQo9Ksl/qiBppqPLmT+Ay1shIdb7Tmq8APJWpO\ntwa9AI9VqLMxKsFvotgy3C1lAkC+EiKNHPsneCVFozNsBLCimw1btRN1VFLGgCkFsKqJfgeoaqIZ\nUEWWKU93I31Ut3jnKZrTQx+BNLD3YJRDxTVr0AyN4QewJHWFwi5/rRg+AijaEKM9GKUpqIvRPvwA\nNLE/5YcGW9R0ja+L0STYrLRJEWBYjBo4PYrzsDiGvkFeLflVHA3p0RlzcLlK10sCBtlIFtVWMN3C\nHwc4KEcjMNue1IR6Trn4njWjltJY2VETRo58yALMqIu/12yd8hd0Fkp82+Ha1FcSKlSoUKH+TaCt\n/4+GChVqE8m46jUX5/bbL6a+BaA3vcb1fHtRjwbcRz3X8NsAUwv0Hg8vvddG24PG7Zbx30PZWe7m\nvMvX7Mps/EldB0y6H3YtXPb3xeLwxh0A/MJ+pLG9yKNnGxaySO64/92h52XiQbNr2IXxfUAejXfu\n2oavEcejfcjOVLwehUcnVnibWhajGagz67OFooNitIKMSdPcDYvREgozTTksi9EiilASPK0CP+p+\naRd4bCKPZtGsXTi1fjSPikTxABHUf1W8Frm1z9IMFtYAeNyXGJ3HxS1HFeXiaQFV9dBmrAp6aI+v\nUyFET/pa3CLUAJ9RFaE0AQ7RQ/PelxKihu231AI05p9UhFYCzH8wmoSAXxiC0XxQqywQjaP+kgJ9\nGPhbRBBqmHyhStAYvCaaaKlhaaLdrEsS3a1AUzU3pQOrcrQXplnPblmOZjp1kilI0Siqk5R8H5h3\nArtXAWjCnkOLRrplnHLwC1oytPg+3dbS0vEif303+SLq4y76de92g0+cLIeu8PEGXBsR3j6w5mI6\n/eVY65OREx/TZbf1hlXt9NmQCuyEQVqXoCaPshK48eC0G+sz94Xt2b/aBM5fGUZy4QAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "5/12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P(X > Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "podoc": {
     "output_text": "5/12"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAACpBAMAAABHSQc1AAAAMFBMVEX///92dnaqqqpUVFQiIiKI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\nrkJggg==\n",
      "text/plain": [
       "5/12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P(X + Y > 6, X < 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = Normal('Z', 0, 1)  # Gaussian variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "podoc": {
     "output_text": "Output"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BQCK6u9z9zgg51wPEpQX/cL+gZd0RdqUEllFRgKFzzoFWZAz4SseyQHLoLzjt\n0PZ4hliX+1BI5p4m4XErNrGMigIMnXNeL15Qmn/CZzSCPi6rpZiirbzI6celFc7R57Q26Bp2tTWW\nUVGA4XOuCZQzM3xAKOjjkllywaGtMMvox6WXua1rpCUNu9iNI7CMigIMn3N1oPvd2JzdsWDJTlb/\n3RNCzqW0ixUcl4tnO/c1TYBbd49kVBxgRXTOlaDH0zW/2VRBYIHBitLEt1RcXT+am3zvy/PxlTe/\n+z6tZxTwL1TjGBUHWBr9TlsGWrVZ9yGVBNGFuzKeS9twt6lbtdnYENuv6TkC7DMWHKPiADshqCUH\nlrimfdL2tiuls+uIok8r0NU1bwoGDnlu6r0U7G6lOEbFAPbOz3pfGfrnt1BZ5wLFkoofNLSnIuNd\nWzsiys9rljTFkuYm53TykBb+RUMco8KBcSsSc3/tQGsi1mpLVtBFtL5+jS3aDm15PbGkEDjI1rkn\nVKNohoBhVDgwIs7Vodeq18JjTjD/wToWqNJ+4DSld606F+DcqcZPdwmkRxSjwoEVnv/8MsH67vO4\nm9IU+oCFCYaCJKm19u5J4g9iuVoGLgU4p/HDWYrGkRhGJQGGtimdQh5QXnmYhiCgyryymrXT+DTp\nPDrM6Ddj/ZHET1txjEoCDG1Tgq2G7iKNqtC27JCIEXbz+yf4/TdwjEoDDCtchQVay+OzNHEX5/jI\nbLyTHx6SnLAgGHVIe/QDGQPoodyypqO+2+ChvKudpEmSkCMYtcl26wWiXTBsU0ouNIb+joOH7o4i\n5i5J+2oEo3bpP9euOzLQwr7U/J5SivqDV5Yu6wrN14LhRq3Qf8YYNDuYitH3zjqTxB+CkUkiHu3g\nZ4tEcSTYqMVdBbgyowEt4R16CdJo1448Tf45y7DAi6QhPNioI/LP3gFGC5pEeGL+aW3XWlB2N0lE\nh2hLBxu1Y28KMde8YUmEd2j5dYwv0cCGu5MkwiWK1MFGde1NIeYqwxRs96c7OgXgxoD2yoVp7wo0\natbaU4j5AH/EZcAY7bUuqVEl/4aqOFK/R7aEIEalA4YyatDSthNmQ16e3IWVR2THvECjjtjud55o\nlQGWRHgF7k93Po3ULnaTDpmDBxq1Y8HOE+0gYHquw6xYVLUdRM1dsj4sQKN2ib96B3cQE/DbvrL7\nedTNqwNZQuEVZNSszYrwcnZn0LdtwaJKmi9nyhEefoCMmtvNqYxSvAlzEEUrKrUcRnufUTBahA4e\nZNSWFTtPdLgKOyap2JEjNYm/Fr092oQOHmTUtt3h3NxBAFXhL92wYR4j06pwljRfBxg1a4OQEOsg\nbiT2f2TAVcFyAAAB6klEQVRMV8bmbBXBcnarc964Q3sR0Ji/7hpO1lq2nmm2bD5sXYy8vaXzSqNj\n2F+3mf8dBauGtcC44RrP+EhGyaxCl2W7veu2f8D4MbTfF8ulekYr5Eu7qGTZa2D8SLJdl5bjjJrR\nI9eOrYJEx3alZBl9Pz0Ezt0xebLt2Fou5Nhdx7QavX1YGfGjYLKGrmhr9XfR5rJ0f6QPQy1JNAyq\nJUPitj+HB2xzpA5ELakbVEtcW+MRd08Cpc4eKDoSI8/Yq4Z+qmzupw4EWHDk7K4rlR5tY2t8ZOuB\n4WhfTjKPm6t66GjpDtbYGw2idxiba8HUxlK2VXct74MgvBjJA9lca4ZWed1Wdam+R7KXexiba8nQ\n5tq2tR1I2+I+Jdvr4yA215SZzTVv67aQ36f9qnwgm+vAyOZax/4K1sEDE47+HhTASIyikV45rq2F\nuK71FcL8yB3GmessoHnPBLGv2rriru7Ru3LcPdGvY8bbBgLTga17wmDPNqvL1n5QQC2L6JLf7azY\nGvtW9i0orxxGtXBiSF4tfMfWzgx3LG8ZsT16ljcckBwF8pimwV60c+rWAgsdeXvbuyuNDnHulmHT\nCysnbi2wiFGzvMuF5EgSB6YjW5Ot0R5mgYWPXT0EziX++jdIH1/+vKXbQQiw/wcz8kyV3wGt5gAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "Output"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P(Z > pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "podoc": {
     "output_text": "(1, 2)"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAABTBAMAAACrE2wWAAAAMFBMVEX///92dnaIiIhUVFSYmJgi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\nrkJggg==\n",
      "text/plain": [
       "(1, 2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "E(Z**2), variance(Z**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = density(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "podoc": {
     "output_text": "Output"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASMAAADnBAMAAACnAC0IAAAAMFBMVEX///9mZmbc3NxERER2dna6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\nAElFTkSuQmCC\n",
      "text/plain": [
       "Output"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var('x')\n",
    "f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x7f775c9c6da0>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w68ChM6JCHHq6A4HNkj3lKrLJWwEA9F0EIgAQhEzT1I+2l6rO5nP+lIFh+u6F3vuBdNWM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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f775c9c6da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plot(f(x), (x, -6, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "podoc": {
     "output_text": "Output"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NKrOfmT++RGp0Aqnj0q6g4QM8oSEilDvlXvlRIhQSj5gU0HPodSoJUQ7m3v5J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\nkgldqbxxhebHp74cYMe7/wcxr4runhwbSgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Output"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eq(Integral(f(x), (x, pi, oo)),\n",
    "   simplify(integrate(f(x), (x, pi, oo))))"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}
